Question

Atlas Company is investigating three approaches to production. Approach A entails buying a $25,000 machine that will last 7 years and will have no salvage value at the end of those 7 years. Annual production costs for Approach A are estimated at $0.20/unit. Approach B entails buying a $35,000 machine that will have a salvage value of $2,000 at the end of its 7-year lifetime and incurring annual production costs of $0.15/unit. Approach C involves purchasing a machine for $30,000 that will be sold at the end of its 7-year life for a salvage value of $2,000. Approach C will incur annual production costs of $0.25/unit. The company uses a 15% interest rate. Determine for each approach the range of annual units that would need to be produced for this approach to be the most cost-effective one.

Answer 1

It is a fact that at lower level of production, machine with a lower fixed cost is preferred over a machine with higher fixed cost.

Since the slvaege value for both machines is $2,000 after 7 yesr, we find PV of the same ar 15% p.a. for 7 years as $752 ($2,000*0.3759).

Thus machine cost for machine B and MAchine C can be considered as $34,248 and $29,248.

The we find breakeven points for all three pairs taking number of units to be produced as x

A & B:

25,000 + 0.2x = 34,248 + 0.15x gives x as 184,960.

B & C:

34,248 + 0.2x= 29,248 + 0.25X gives x as 50,000

Note that in case of A and C, A will always prevail since it has a lower fixed cost as well as a lower variable cost.

Thus upto 50,000 units Machine A is better.

Between 50,000 units and 184,960 units Machine C and A both are better than B but A will prevail.

Pver 184,960 units machine C is better.